The 26-year-old, who scored 40 goals in 139 appearances for the Serie A side, links up again with new Swans manager Francesco Guidolin after a previous stint together at Parma.
"I'm very happy to be here," Paloschi told the club's official website. "I worked with Francesco for two seasons at Parma and we got promoted. When I received a call from my agent to tell me that Swansea were interested it was great, but even more so because of the manager - it makes a big difference.
"I know the situation of the club and, being a striker, I know the expectation is to score goals and I've come here to do that."
Paloschi will wear the No.9 shirt for the Welsh side, who sit 15th in the Premier League.